The Maximization of Falsifiability: How To Acquire the Logic of Implicatures from The Illogic of Experience
Tom Roeper
UNIVERSITYOF MASSACHUSETTS
1.0 Introduction to an Intricate Interface
Deductive reasoning requires precision in the definitions of logical words.The word “logic” itself refers to that notion, although in daily life the term“logical”, like virtually all words, is used with pragmatic ambiguity and evenwilful imprecision. The pragmatic force of real life situations is very important when one addresses the acquisition question: how does a child’s innate knowledge mesh with experience in order to lead to the understanding of particular grammars.
The discussion to follow originates in elementary reasoning about how we shouldconceive of the acquisition path. It does not reflect a thorough background in philosophy, logic, the evidence of how implicatures work, nor a thorough study of adult uses of logical terms, nor a much-needed careful study of how children use logical terms in naturalistic contexts beyond experimental contexts. An acute application of what is already known will, one hopes, enhance the claims to follow, but may challenge them as well. This discussion should be seen as a prolegomena to the study of these questions, and a plea for pursuing one angle on that interdisciplinary research.[１]
Learnability theory needs to be conceived of with sufficient intricacy and sensitivity to meet the actual kinds of variation that children experience every day. The argument below is that the concept of Maximization of Falsifiability (MaxF) is ideally suited to the task. This paper follows the theory of Anna Verbuk: that MaxF can apply to the interface between pragmatics and semantics. I will present and expand upon a few of the core examples in her work and seek to orient it in a larger context.
Where do the complexities of real life entangle the acquisition process? One place is the difficult dividing line between pragmatics and semantics (Levinson (2000)). For instance, as we shall see, while some unusual properties of quantifiers might simply be considered forms of “pragmatic strengthening ” for adults and therefore irrelevant to the core definition of logical terms, it may not be immediately evident to the child that a property of pragmatics is not a property of the semantics and therefore required in any exercise of deductive logic, independent of context. The claim here is that a child’s apparent errors may reveal more strict deductive reasoning than adult’s reasoning precisely because their definitions of crucial terms may, briefly, carry stronger restrictions.
It appears that languages vary in what information is
included in quantificational terms. Terms in Dutch like “allemall” vary across the meaning “often” “all the time” and “all kinds”.[２]Terms like “all the time” in English can mean either constantly or repeatedly. Acquisition of such terms requires a lot of subtle work by children and a capacity to register the nuances of triggering experiences.
1.1 Maximization of Falsifiability
Edwin Williams (1981) advanced an important idea for learnability theory: the Maximization of Falsifiability (MaxF). The claim is that:
(1) a. A child’s initial representations (definitions) of words and nodes are as rich as possible.
(1) a. A child’s initial representations (definitions) of words and nodes are as rich as possible.
Definitions which are too broad are compatible with too many interpretations, while highly specific definitions are quickly contradicted by experience. In a word, vague or incomplete representations are the enemy of learning. The impact of negative information, which can change grammar, is strongest when the definition of words are too precise and restrictive., which we will illustrate shortly. In that sense, this theory adheres to the logic of the Subset principle at the semantic level. (See Berwick (1985), Crain and Thornton(1998)). New information expands the number of sentencesthat the grammar accommodates by reducing grammatical restrictions, which in turngradually makes the rules more abstract.
Here is a little illustration of how it can work, and how quickly it can work.Suppose the child hears either den (German) or the in front of a noun. Let the child guess that it is an article. How should she determine its properties. Suppose in bothcases the child makes the Maximal assumption about possible features associatedwith articles (probably there are more than these in fact)
(2) a. English Child I saw the man
Masc
Sing
Accusative
Definite
b. German child: Ich sah den Mann
Masc
Sing
Accusative
Definite
The German child will be immediately right. The English child quite wrong, butthe Hypothesis lends itself to contradiction. In five minutes the child might hear“I saw the woman” which cancels the gender feature, then “I saw the girls” whichcancels the singular feature, and then “The girls came” which cancels the accusative feature leaving only definiteness.There is no reason not to believe that a great deal of micro-acquisition occurs—within a few hours---much like manysteps in the mastery of bicycle balance occur in the few minutes after a childmanages to stay on a bike. If the opposite strategy is assumed—the/den = onlydefiniteness--then the English child will be right, but the German child willfreely use den in nominative positions and with plurals, etc. What will forcea change. Hearing Der (nominative) Mann is a nominative form, but alsocarries demonstrative force, and therefore it might not be seen as an alternativeblocking the use of den. The child could easily continue with the assumption thateither der mann or den Mann is acceptable. The conditions for revision are far more obscure if one seeks to add features.
It is interesting to ask how far MaxF can be applied. Not only syntax butimplicatures, as we will show, and also,following Verbuk and Roeper (2006) the acquisition of Principle B in binding theory can be understood from this perspective.Nevertheless, the concept of Maximization of Falsifiability itself is an idealization that is surely too strong. There must be contexts where a child does add to the definition of words as well as subtract from them and at least a few contexts where acquisition depends upon comparison of words and an application of the “uniqueness” assumption that words have differentmeanings.
1.2 Innate Logic
A strong and important claim has been advanced by Cherchia (2004): in essence,the principles of logic are innate and therefore a) require no learning, and b) instantlyengender implicatures which are implicitly or explicitly computed all of the time.Acquisition evidence (Papafragou (2006) and, Guasti et al (2004) , and others) have suggested that the implicature consequences of these principles by children are not immediately realized.Therefore it could be that the entire capacity for computing implicatures must be triggered or mature, or become available via an interfacecomputation (see Reinhard (to appear), although mixed evidence leaves such a conclusion rather murky. Others (Papafragou and Tanatalou (2004), Papafragou (2006)) have claimed that the implicatures involving “world knowledge” are particularized in a way that slows their acquisition. Horn (2005) argues that pragmatics is present everywhere.
We will argue that the range of possible definitions of words with logical force within Universal Grammar is much larger than usually supposed. Consequently the task of isolating the logical force of words is not straightforward and requires subtle, and pragmatically exact experiences.Nevertheless deductive reasoning must eventuallybe possible---even against pragmatics---and it supplies us with the capacity to, forinstance, build atheory of linguistics where grammaticality can be identified withoutthe requirement of compatibility with context.The argument here is that the childmust, in some domains, move from a restrictive pragmatic definition to a broadersemantic one. It could be an implicit goal of growth, belonging to the whole species,to find definitions that allow strict deductive reasoning free of pragmatic qualifications. To put it differently, the efficiency of language in general lies largely in guaranteeing meanings that areindependent of context and which can even support anti-pragmatic readings (see Hollebrandse and Roeper (to appear)). Sentences like:
(3) John met every person in the world
have a meaning which is impossible. but its meaning is computed as fast as any other sentence---as well as its implausibility, without any particular context needed.
1.3 Inference and Implicature
Horn (2005) and Papafregou (2006) argue and provide evidence that children can undertake particularized situational implicatures. We argue that some of these implicatures belong to General Inference which is needed to see what is not said, to infer motives, in every conversation, and in many non-verbal situations. They should be kept distinct from implicatures that are properties of words which are immune to pragmatic modification. General inference, while deep and complex, computes plausible, not implausible consequences of situations.
In contrast, a statement like the following has a logical implicature whether we can make sense of it or not:
(4) Some people are people.
implies automatically that Not all people are people, a conclusion with which we have to struggle cognitively, using any kind of inference, including a strong sense of irony orcynicism, to rescue from apparent nonsense. Nevertheless the implicature is present.
While it might seem counter-intuitive at first, it is really quite plausible toargue that children bring enormous inferential capacities to the earliest stages ofacquisition. In effect, when a sentence is not understood, one tries to make inferences from individual words to possible meanings. This occurs at theone-word stage. Every utterance requires an interpretation for why it is said. The interpretive demand is greater if your grammar is smaller. The child who hears:
“Milk!”
must be able to translate it into a range of meanings like “do you want somemilk” or “be careful and don’t knock over the milk carton” using a lot of inferentialpower.
2.0 Projecting Restrictors
It is a fundamental feature of quantification that it carries
both overt and covert restrictors:
(5) every child must wear a bathing suit
The quantifier every (Heim (1988)) is restricted by the noun childand by some property of the context, such as, in this class.
Now we can ask: what constitutes a possible restrictor and howfar does it get built into the quantifier itself. Here is where onecan be unsure of what is entailed. Elementary time and locationrestrictions appear to be present without much contextual demands:
(6) the boy wearing a red shirt stole the fruit yesterday.
This sentence can mean a boy wearing the red shirt now or a boywearing a red shirt during the robbery. A kind of optional default restriction to Here and Now seems to be present in many circumstances.
Are there others? Piaget originally proposed that children cognitively presupposed “simultaneity” in various tasks, but Schmiedtova (2004) has shown that young children have the capacity to make the distinction between what is simultaneous and what is not. We argue that the phenomenon is not a cognitive unit but a part of the system whereby implicatures are calculated. It fits the MaxF systematic effort by children to over-restrict meanings in order toultimately isolate the correct meaning.Apparent misapplication of simultaneity could be seeking an implicature where none is present, although perhsps it sometimes is. Consider this case:
(7) Here are 500 bricks. Can you lift all of them?
The natural answer is “no, they would be too heavy”. But notethat there is an implication of “all at once” that is not logically necessary. Surely one could lift them one by one. Many situations are open to an ambiguity here:
(8) a. Could you carry all your toys to your room?
This could mean all separately or all at once. Anna Verbuk reports (to appear) that children often reveal their restrictions in overt conversation. One 4.11 yr old child was asked if one animal had scratched all of another’s body and responded (“a card” means “no”),
(8) b. A. (4;11): A card. Because he didn’t do it all at once. Cause he (=Tiger) was asking him (=Deer) to do it (=scratch Tiger’s body) all at once, even though he didn’t say, “do it all at once
Many others offer similarly complex reasoning. From the perspective we are pursuing, the child is doing precisely the correct thing: he is maximizing the possible features associated semantically with “all”. The adult, by contrast, has this meaning asan implicature, a part of Pragmatic Strengthening if the context calls for it. It is not a part of the meaning of all when we engage in deductive reasoning.
Could this meaning enter the logic of how quantifiers areinterpreted elsewhere? Papafragou and Tantalou (2006) gave children sentences involving some whose implicature should be not all. They weregiven a scene of this general kind:
(9) 1. First two animals jump over the fence
2. Then another animal jumps over a fence
3. Then a third animal jumps over a fence
When 6 year-olds were asked:
(10) “Did some of the animals jump over the fence”
they answered “yes” while adults answered “No”. This has been takento mean that the children have not been able to process the implicature.However they are surely aware that all the animals have jumped overthe fence and this implicature is far less complicated than many inferencesthat are implicitly made by toddlers.
If however children have applied the logic of MaxF to some aswell as all, then we make precisely the correct prediction about thechildren’s “yes” answer as seeking a restrictor that allows “yes”:
(11) Did some of the animals jump over the fence at once?
Put in as a restrictor it would be:
(12) Did “some at once” of the animals jump over the fence?
If this logic holds for a wide variety of implicatures, then we willexpect the process to involve a great deal of quite specific experience.There are interesting examples that suggest that children mightentertain quite unusual restrictors that apply in the domain of comparativesas well. Consider this dialogue from the Adam Files of Childes:
(13) Ursula: its much bigger
Adam: it’s much smaller too
Ursula: it’s much smaller!
how can it be both!
Such forms of differentiation are not unknown in the adult language, but there is a default notion that bigger/smallerapplies to the whole object. If the tail were bigger and thehead were smaller we might say “one is both bigger andsmaller than the other” with the implication to search forrestrictions that would render the sentence non-contradictory.
Now let us imagine what the range of possible restrictors couldbe for one quantifier: all. Then we will provide the kinds of experience which force thechild to drop those excessive restrictors.
2.1 Kinds of All
The following are examples of possible extensions of the
meaning of all:
1. Kind: all = all kinds
a. we have all Toyotas on our lot.
2. Variety: all = any possible selection
a. we have all nationalities at Umass.
3. Collective: all = group action
a. we all lifted the table
4. Exclusive: all = all and only (possible, but not English)
a. he picked up all the toys.
5. Adverbial: all = completely
a. he ran all the way around the house
6. Adverbial: all = isolated (?)
a. he sat all by himself.
7. Quotation: all = enthusiastic attribution
a. he was all “I can do it”
All of these example sentences are not far removed from the languageof parents to children. It would be useful to do a study and see exactlywhich ones occur.
The common property of all is assumed to be exhaustivity. Is this property reliably honored? Consider a situation like this:
(14) [5 of 50 students are present at the start of class]
Someone says with disdain:
“all the students come late to this class”
If a child hears some version of this sentence, spoken with commonexaggeration, he is entitled to assume: all = most. This would be a difficult assumption to overturn since in every situation where all is used, it would also be true of most.
How can we block such a modification? A careful look at theconcept of restrictor suggests that it must indeed restrict. Suppose we triedto add a restrictor of the general form roughly speaking—to capture moments of casual overstatement--- to any quantifier.
This move would render the quantifier vague in a way that most conceivable evidence could not rescue. By our logic, it would make language unlearnable. Therefore the possible restrictors must themselves be constrained. To state it informally: restrictors must restrict and not expand the relevant domain.
It is quite possible that there is a further range of restrictors that apply which we have not seen and which, being short-lived, do not exhibit themselves overtly in the acquisition process.
2.2 Triggering Progress
Children have many informative experiences. The child who
might briefly entertain the idea that all = most would surely have some corrective experience, which imposes exhaustivity:
(15) [two of twenty toys are not picked up by a child]
“you didn’t pick up all your toys
Similarly if the child assumed, which does not seem unnatural, that
all = all and only, experiences would arise, where one says: